{"id":"https://openalex.org/W2162128145","doi":"https://doi.org/10.1137/s0097539791201587","title":"Polynomial Root-Finding Algorithms and Branched Covers","display_name":"Polynomial Root-Finding Algorithms and Branched Covers","publication_year":1994,"publication_date":"1994-04-01","ids":{"openalex":"https://openalex.org/W2162128145","doi":"https://doi.org/10.1137/s0097539791201587","mag":"2162128145"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539791201587","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539791201587","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/9201280","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Myong-Hi Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Myong-Hi Kim","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Scott Sutherland","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Scott Sutherland","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9311,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.77565707,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"23","issue":"2","first_page":"415","last_page":"436"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9513999819755554,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9513999819755554,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.0272000003606081,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.005799999926239252,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5566999912261963},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.550000011920929},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.427700012922287},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.40310001373291016},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.37070000171661377},{"id":"https://openalex.org/keywords/square-free-polynomial","display_name":"Square-free polynomial","score":0.3626999855041504},{"id":"https://openalex.org/keywords/reciprocal-polynomial","display_name":"Reciprocal polynomial","score":0.3154999911785126},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.301800012588501}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6462000012397766},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5566999912261963},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.550000011920929},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.498199999332428},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46160000562667847},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.453900009393692},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.427700012922287},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.40310001373291016},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.37070000171661377},{"id":"https://openalex.org/C101525915","wikidata":"https://www.wikidata.org/wiki/Q7581979","display_name":"Square-free polynomial","level":4,"score":0.3626999855041504},{"id":"https://openalex.org/C97395012","wikidata":"https://www.wikidata.org/wiki/Q1422356","display_name":"Reciprocal polynomial","level":4,"score":0.3154999911785126},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.301800012588501},{"id":"https://openalex.org/C45025165","wikidata":"https://www.wikidata.org/wiki/Q13424738","display_name":"Stable polynomial","level":5,"score":0.2953999936580658},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2849000096321106},{"id":"https://openalex.org/C64731005","wikidata":"https://www.wikidata.org/wiki/Q333464","display_name":"Analysis of algorithms","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.2694000005722046},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C131583701","wikidata":"https://www.wikidata.org/wiki/Q7625020","display_name":"Structural complexity theory","level":4,"score":0.2614000141620636},{"id":"https://openalex.org/C30597210","wikidata":"https://www.wikidata.org/wiki/Q1163608","display_name":"Minimal polynomial (linear algebra)","level":5,"score":0.25600001215934753},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2551000118255615}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0097539791201587","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539791201587","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/9201280","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/9201280","pdf_url":"https://arxiv.org/pdf/math/9201280","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/9201280","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/9201280","pdf_url":"https://arxiv.org/pdf/math/9201280","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W235157351","https://openalex.org/W1571614612","https://openalex.org/W1590743980","https://openalex.org/W1969285485","https://openalex.org/W1982522946","https://openalex.org/W2003085352","https://openalex.org/W2003933590","https://openalex.org/W2004272409","https://openalex.org/W2005485993","https://openalex.org/W2023380241","https://openalex.org/W2029950920","https://openalex.org/W2039897960","https://openalex.org/W2052645364","https://openalex.org/W2060935972","https://openalex.org/W2077918470","https://openalex.org/W2111468049","https://openalex.org/W2144493917","https://openalex.org/W2161829873","https://openalex.org/W2592503220"],"related_works":[],"abstract_inverted_index":{"A":[0],"family":[1,29],"of":[2,10,15,39,42,50,73],"root-finding":[3],"algorithms":[4],"is":[5,67],"constructed":[6],"that":[7,33,45],"combines":[8],"knowledge":[9],"the":[11,28,62,68,74],"branched":[12],"covering":[13],"structure":[14],"a":[16,19,40],"polynomial":[17,41],"with":[18],"path-lifting":[20],"algorithm":[21,32],"for":[22],"finding":[23],"individual":[24],"roots.":[25],"In":[26],"particular,":[27],"includes":[30],"an":[31,35,47],"computes":[34],"$":[36],"\\epsilon":[37,54],"$-factorization":[38],"degree":[43],"d":[44],"has":[46],"arithmetic":[48],"complexity":[49,66],"$\\mathcal{O}(d(\\log":[51],"d)^2":[52,59],"|\\log":[53],"|":[55],"+":[56],"d^2":[57],"(\\log":[58],")$.":[60],"At":[61],"present":[63],"time,":[64],"this":[65],"best":[69],"known":[70],"in":[71],"terms":[72],"degree.":[75]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2016-06-24T00:00:00"}
